Fifty-five colleges and universities have signed on to participate in a program run by two prominent nonprofits to examine how well the schools are handling student mental health on campus, the organizations plan to announce Wednesday.

The schools on the list are taking part in the The Jed & Clinton Health Matters Campus Program, a partnership of the Jed Foundation, a nonprofit that promotes mental health at colleges and universities, and The Clinton Foundation Health Matters Initiative, which is part of the Bill, Hillary & Chelse...